By stating fastest moving creatures, I'll assume you're referring to all animals, be it land, air or sea animals. In saying so, it's really going to be difficult choosing a particular animal as the fastest.
Comparing the speed of one man to another is quiet understandable as all humans belong to the same group. But even the speed of a minor can't be compared with that of an adult. Hence, drawing a comparison between the speed of an ant with that of a mouse is way out of proportion. This is the reason why bringing together and considering different animal categories to get one compared result isn't possible. There's the difference in their nature, am talking about sizes and body, as well as the different animal groups they belong to.
However, there's a list of the fastest animals from the different categories they belong to. The fastest Land animal is Cheetah, with a recorded speed of 109.4 - 120.7 km/h.
The fastest animal in air is the Peregrine Falcon with a recorded diving speed of 389 km/h. This bird is largely classified as the fastest animal on the animal kingdom.
The fastest animal in water or sea will have to be the Black Marlin with a recorded speed of 129 km/h.